Oh god. That's a good question / thought experiment (edit: okay, maybe not exactly as stated), but how long will it be before the headline "Vaccines cause cancer" starts making the rounds on Facebook?

Might it be possible that there could be one vaccine who's risks outweigh its benefits? Or are all vaccines completely safe and effective and that's the end of the story forever?

do you believe that's the way the argument is positioned by the majority of "anti-vax" people?

We're safe, because there is no cold vaccine.

No, but we have many other vaccines and some crackpot could make up some fake data claiming that vaccines cause cancer and that we never had all this cancer back in the "good old days" before vaccines were invented.

You mean when everyone was dead long before the cancer could've had a chance to kill them?

You're thinking much too logically; these people will either deny basic facts or base their opinion on something completely disproven, in order to cling to their opinion.